The Mojette transform is a tool for discrete tomography. An image can be recovered exactly from a set of its discrete projections. In this paper, we define algorithms to perform exact, reversible and scale change rotations in the Mojette space, taking advantage of its inherent rotational structure. The whole process is thus achieved by a series of 1D operations on each Mojette projection, reducing the complexity problem. The inverse operation is similar to the direct rotation with opposite angle and inverse scale factor.